Anatomy of a small intraplate earthquake: a dissection of its rupture characteristics using regional data

The magnitude m _bLg 5.0 Mont-Laurier earthquake of 1990 October 19, in Quebec, Canada, was one of the largest to have occurred in eastern North America during the past decade. High-frequency ground motions recorded on regional network instruments exceeded values anticipated for an event of its size by a factor of 3. A commonly favoured explanation for the discrepancy is that the source was a rare 'high-stress' event. In this paper, detailed fault-slip models are derived to fit waveform and spectral characteristics of the regional data. The results establish that the effective rupture stress was normal (about 100 bars), that the fault rupture developed asymmetrically, and that the average slip time for points inside the rupture area (approx. 0.1 s) was significantly less than that associated with the standard Brune (1970) source spectral model. The rupture area developed in at least four distinct episodes, each extending the previously ruptured area. Taken together with similar results for the m _bLg 6.5 Saguenay earthquake of 1988 November, the results indicate that a widely used assumption in hazard analyses, that earthquake spectra are adequately represented by the standard Brune spectral model, is unreliable for the interpretation and prediction of strong ground motion.     

Coupled normal-mode sensitivity to inner-core shear velocity and attenuation

We have studied the response of normal modes to perturbations in inner-core shear velocity and attenuation, using fully coupled mode synthetics. Our results indicate that (i) mode pairs   _n S _l – _{n ±1} S _l   are strongly coupled by anelasticity, (ii) this coupling causes shear velocity perturbations to strongly affect the Q values of modes through exchange of inner-core characteristics, (iii) there is no evidence for a weakly attenuating inner core in shear, and (iv) the discrepancy between attenuation models returned from normal modes and body waves is small. These results suggest that inversions for inner-core attenuation and shear velocity should be performed simultaneously and should take account of the strong cross-coupling due to attenuation.     

Three-dimensional VP and VP /VS models of the upper crust in the Friuli area (northeastern Italy)

3-D images of P velocity and P - to S -velocity ratio have been produced for the upper crust of the Friuli area (northeastern Italy) using local earthquake tomography. The data consist of 2565 P and 930 S arrival times of high quality. The best-fitting V _P and V _P / V _S 1-D models were computed before the 3-D inversion. V _P was measured on two rock samples representative of the investigated upper layers of the Friuli crust. The tomographic V _P model was used for modelling the gravity anomalies, by converting the velocity values into densities along three vertical cross-sections. The computed gravity anomalies were optimized with respect to the observed gravity anomalies. The crust investigated is characterized by sharp lateral and deep V _P and V _P / V _S anomalies that are associated with the complex geological structure. High V _P / V _S values are associated with highly fractured zones related to the main faulting pattern. The relocated seismicity is generally associated with sharp variations in the V _P / V _S anomalies. The V _P images show a high-velocity body below 6 km depth in the central part of the Friuli area, marked also by strong V _P / V _S heterogeneities, and this is interpreted as a tectonic wedge. Comparison with the distribution of earthquakes supports the hypothesis that the tectonic wedge controls most of the seismicity and can be considered to be the main seismogenic zone in the Friuli area.     

High-frequency radiation from crack (stress drop) models of earthquake faulting

We present a theory for the radiation of high-frequency waves by earthquake faults. We model the fault as a planar region in which the stress drops to the kinematic friction during slip. This model is entirely equivalent to a shear crack. For two-dimensional fault models we show that the high frequencies originate from the stress and slip velocity concentrations in the vicinity of the fault's edges. These stress concentrations radiate when the crack expands with accelerated motion. The most efficient generation of high-frequency waves occurs when the rupture velocity changes abruptly. In this case, the displacement spectrum has an ω^-2 behaviour at high frequencies. The excitation is proportional to the intensity of the stress concentration near the crack tips and to the change in the focusing factor due to rupture velocity. We extend these two-dimensional results to more general three-dimensional fault models in the case when the rupture velocity changes simultaneously on the rupture front. Results are similar to those described for two-dimensional faults. We apply the theory to the case of a circular fault that grows at constant velocity and stops suddenly. The present theory is in excellent agreement with a numerical solution of the same problem.
Our results provide upper bounds to the high-frequency radiation from more realistic models in which rupture velocity does not change suddenly. The ω^-2 is the minimum possible decay at high frequencies for any crack model of the source.     

Focal mechanisms of recent earthquakes in the Southern Korean Peninsula

We evaluate the stress field in and around the southern Korean Peninsula with focal mechanism solutions, using the data collected from 71 earthquakes ( M_L = 1.9–5.2) between 1999 and 2004. For this, the hypocentres were relocated and well-constrained fault plane solutions were obtained from the data set of 1270 clear P -wave polarities and 46 SH / P amplitude ratios. The focal mechanism solutions indicate that the prevailing faulting types in South Korea are strike-slip-dominant-oblique-slip faultings with minor reverse-slip component. The maximum principal stresses (σ₁) estimated from fault-slip inversion analysis of the focal mechanism solutions show a similar orientation with E–W trend (269°–275°) and low-angle plunge (10°–25°) for all tectonic provinces in South Korea, consistent with the E–W trending maximum horizontal stress (σ_Hmax) of the Amurian microplate reported from in situ stress measurements and earthquake focal mechanisms. The directions of the intermediate (σ₂) and minimum (σ₃) principal stresses of the Gyeongsang Basin are, however, about 90 deg off from those of the other tectonic provinces on a common σ₂–σ₃ plane, suggesting a permutation of σ₂ and σ₃. Our results incorporated with those from the kinematic studies of the Quaternary faults imply that NNW- to NE-striking faults (dextral strike-slip or oblique-slip with a reverse-slip component) are highly likely to generate earthquakes in South Korea.     

New approach in the kinematic k−2 source model for generating physical slip velocity functions

In an attempt to improve the ground motion modelling, the characteristics of the slip velocity functions (SVF) generated using the kinematic k ⁻² source are investigated and compared to the dynamic solutions proposed in the literature. Several numerical simulations were performed to test the influence of the model parameters on the SVF modelling. Overall, the shapes of SVF are very complex and exhibit a large variability in time and space. However, we found out that the mean SVF is a simple boxcar with duration equal to the largest rise time value. In the areas of weak slip, the SVFs are characterized by the existence of negative values, whereas in large slip areas, the SVF is more impulsive. Overall, on the examples investigated, the SVFs modelled with this k ⁻² source model are different from a typical Kostrov's solution. The critical analysis of the kinematic k ⁻² source led us to identify the Fourier decomposition of the slip to be responsible for these difficulties, and to propose a new recombination scheme. It consists of adding a positive correction to the Fourier slip components. The slip is described as the sum of positive contributions at various scales. The SVFs modelled using this new scheme are greatly improved. Moreover, through several parametrical analyses performed to qualify this new approach, we show that the SVF are corrected while preserving the essential quality of the k ⁻² modelling, that is, the ω² spectral shape and C _d apparent directivity of the synthetic accelerograms. Strong ground motion modelling in the near-fault region was made and numerical ground motion parameters were compared to the empirical relationships. We show that predicted peak ground motion is consistent with near-source attenuation laws.     

A note on the surface volume change of shallow earthquakes

Summary. This note presents an exact analytical formula for determining the magnitude of coseismic surface volume change (δ V ) of earthquake faults in a half-space. For a Poisson solid, the formula is remarkably simple; δ V = M _zz |8μ, where M _zz is one of the moment tensor elements of the source. Maximum δ V values derive from dip slip on faults plunging 45°. For these events, surface volume changes of 0.0001 and 4.3 km³ can be expected for magnitude 5 and 8 earthquakes respectively. All of the coseismic surface volume change is recovered in the interseismic period through relaxation of the Earth and rebound of the surface. A useful rule of thumb for estimating the magnitude of vertical rebound in 45° dip slip events is δ h _p=Δ s /24, where Δ s is the coseismic slip on the fault.     

Surface motion of a fluid planet induced by impacts

In order to approximate the free-surface motion of an Earth-sized planet subjected to a giant impact, we have described the excitation of body and surface waves in a spherical compressible fluid planet without gravity or intrinsic material attenuation for a buried explosion source. Using the mode summation method, we obtained an analytical solution for the surface motion of the fluid planet in terms of an infinite series involving the products of spherical Bessel functions and Legendre polynomials. We established a closed form expression for the mode summation excitation coefficient for a spherical buried explosion source, and then calculated the surface motion for different spherical explosion source radii a (for cases of   a / R = 0.001  to 0.035, R is the radius of the Earth) We also studied the effect of placing the explosion source at different radii r ₀ (for cases of   r ₀/ R = 0.90  to 0.96) from the centre of the planet. The amplitude of the quasi-surface waves depends substantially on a / R , and slightly on   r ₀/ R   . For example, in our base-line case,   a / R = 0.03, r ₀/ R = 0.96  , the free-surface velocity above the source is 0.26 c , whereas antipodal to the source, the peak free surface velocity is 0.19 c . Here c is the acoustic velocity of the fluid planet. These results can then be applied to studies of atmosphere erosion via blow-off caused by asteroid impacts.     

Source tomography by simulated annealing using broad-band surface waves and geodetic data: application to the Mw= 8.1 Chile 1995 event

We invert surface-wave and geodetic data for the spatio-temporal complexity of slip during the M _w =8.1 Chile 1995 event by simulated annealing. This quasi-global inversion method allows for a wide exploration of model space, and retains the non-linearity of the source tomography problem. Complex source spectra are obtained from 5 to 45 mHz from first- and second-orbit fundamental-mode Rayleigh waves using an empirical Green's function cross-correlation technique. Coseismic displacement vectors were measured at 10 GPS sites near Antofagasta. They are part of a French-Chilean experiment which monitors the Northern Chile seismic gap. The spectra, together with the geodetic data, are inverted for the moment distribution on a 2-D dipping fault, under the physical constraints of slip positivity and causality. Marginal a posteriori distributions of the model parameters are obtained from several independently inverted solutions. In general, features of the slip model are well resolved. Data are well fitted by a purely unilateral southward rupture with a nearly uniform velocity around 2.5–3.0 km s⁻¹, and a total duration of 65 s. Several regions of moment release were imaged, one near the hypocentre, a major one 80 km south of it and a minor one 160 km south of it. The major patch of moment release seemed to have propagated to relatively shallow depths near the trench, 100 km SSW of the epicentre. The region of major slip is located updip of the 1987, M _w =7.5 earthquake, suggesting a causal relationship. Most of the slip occurred updip of the hypocentre (36 km), but the entire coupled plate interface (20–40 km) ruptured during the Chile 1995 event.     

Estimation of the Bingham distribution function on nearly two-dimensional data sets

Summary. In cases where directional data, such as palaeomagnetic directions, lie nearly along a great circle, a good approximation to the maximum likelihood estimate of the intermediate concentration parameter k ₂ in the Bingham probability distribution is given by: 2( t ₂/ N ) – 1 = I ₁(1/2 k ₂)/ I ₀(1/2 k ₂), where t ₂ is the intermediate eigenvalue, N is the number of samples, and the I_i are the appropriate modified Bessel functions of the first kind. This estimate, the asymptotic limit as the smallest eigenvalue t ₁→ 0, corresponds to restricting all points to lie on a great circle. The limit is also useful as an endpoint for interpolation, especially since numerical calculation in this region is difficult.     

On the linear relation between mb and Ms for discrimination between explosions and earthquakes

Summary. The statistical capability of the m _b: M _s discriminant for the discrimination of earthquake and explosion populations is examined by application of discriminant functions to a group of 83 explosions and 72 earthquakes in Eurasia. Equations are derived for the probability that an event is an earthquake or an explosion. The positive sign of DIS in the decision index equation, DIS _i = 34.3383 – 11.9569 mb _t + 7.1161 M _si , indicates that the event i is an earthquake. Its negative sign indicates that event i is an explosion. The probability of correct classification for an event, P _i , is related to its DIS _i value, by P _i = [1-exp (DIS _i )]⁻¹, where a large, positive DIS indicates a high probability that an event is an earthquake and a large, negative DIS indicates a high probability that an event is an explosion. The discrimination line M _s = 1.680 m _b– 4.825, or m _b= 0.595 M _s+ 2.872 very successfully separates the explosion population from the earthquake population. The points on this line have an equal chance of being an earthquake or an explosion; moreover, for any event, the distance parallel to the M _s-axis from the point representing that event in the m _b: M _s plane to this line is a measure of the probability for the correct classification of that event.     

Modelling of short-interval silent slip events in deeper subduction interfaces considering the frictional properties at the unstable–stable transition regime

Recent high-resolution observations of crustal movements have revealed silent slip events (SSEs) with propagation velocities of around 10–15 km d⁻¹ and with intervals of 3–14 months along the deeper parts of the Cascadia and Nankai subduction zones. This study develops 2-D and 3-D models of these short-interval SSEs considering the frictional behaviour that was confirmed experimentally by Shimamoto for the unstable–stable transition regime. To represent this frictional behaviour, a small cut-off velocity to an evolution effect is introduced in a rate- and state-dependent friction law. When the cut-off velocity to the evolution effect is significantly smaller than that to a direct effect, steady-state friction exhibits velocity weakening at low slip velocities and velocity strengthening at high slip velocities. At the deeper Cascadia and Nankai subduction interfaces, the pore pressure is inferred to be high because of the dehydration of materials in the descending plate. Under conditions where the pore-fluid pressure is nearly equal to the lithostatic pressure and the critical weakening displacement is very small, short-interval SSEs with propagation velocities and slip velocities of 4–8 km d⁻¹ and  2 − 4 × 10⁻⁷  m s⁻¹, respectively, can be reproduced. The propagation velocity of short-interval SSEs is in proportion to the slip velocity. The results also show that during the nucleation process of large earthquakes, the occurrence of short-interval SSEs becomes irregular because of the accelerated slips that occur at the bottom of the seismogenic zone. Our results suggest that monitoring of short-interval SSEs might be useful for forecasting the main earthquakes.     

Stacking for the frequencies and Qs of 0S0 and 1S0

Summary. Using nine IDA records for the Indonesian earthquake of 1977 August 19, we have formed an optimal linear combination of the records and have measured the frequency and Q of ₀ S ₀ and ₁ S ₀. The frequency was measured using the moment ratio method. The attenuation was measured by the minimum width method and by the time-lapse method. The frequency and attenuation were measured simultaneously by varying them to obtain a best fit to the data. A 2000-hr stack, the sum of nine individual records, for ₀ S ₀ gave a frequency of 0.814664 mHz±4 ppm. The values for the Q of ₀ S ₀ for the three different methods of measurement were 5600,5833 and 5700, respectively. The error in the estimates of Q ^-1 is about 5 per cent for the minimum power method. For ₁ S ₀ a 300-hr stack yielded a frequency of 1.63151 mHz±30 ppm. The values of Q for this mode were 1960, 1800 and 1850, respectively, with an error in Q ^-1 of about 12 per cent for the minimum power method.     

Source mechanism of the deep Colombian earthquake of 1970 July 31 from the free oscillation data

Summary. The method proposed by Mendiguren to determine the source parameters from free oscillation data is applied to the 1970 July 31 deep Colombian earthquake. The results indicate a source propagating horizontally for about 150 km along the lithosphere and cutting across its width. The slab behaves as a guide for source propagation. The horizontal propagation velocity is determined as 3.8 km/s. The intensity of the source grew proportionately to the second power of the propagation distance. This rate of source intensity growth may be interpreted either by a fan-shaped fault model or by a cone-shaped volume source. The average slip and stress drop are estimated as 360 cm and 300 bar for the fault model. For the volume source model the transformational shear strain and stress are estimated as 11 × 10⁻⁵ and 160 bar. There is no evidence of a double couple radiation preceding the P origin time. It is shown that the isotropic and deviatoric components of the moment tensor cannot be uniquely resolved when only observations of a single mode are available. It is observed that, from a statistical basis, the available ₀ S_n data for Colombian shock can be equally well explained by a pure deviatoric source model or by a source model including an isotropic component. Numerical experiments indicate that the inclusion of higher mode data does not change this situation. But, on the other hand, numerical experiments show that the available data and the scheme used for the inversion would not result in a solution including an artificial implosive component if the actual source were pure deviatoric. If the departure from a pure deviatoric source is produced by noise, it has to be non-random, as it could be produced by lateral heterogeneities not included in the inversion scheme.     

Palaeomagnetism of the Fongen-Hyllingen gabbro complex, southern Scandinavian Caledonides; plate rotation or polar shift?

Summary. Palaeomagnetic results are presented from the c . 160 km² Caledonian synorogenic layered Fongen-Hyllingen gabbro complex (of probable late Silurian age) located about 75 km SE of Trondheim, Norway, in the allochthonous Seve-Kdli Nappe Complex. A total of 80 oriented samples from eight sites in the northern part of the gabbro were investigated. After detailed af demagnetization two stable high coercivity components emerge: one with a well defined NW direction with D =325°, I =−21° (α₉₅=8°, N =8), and another, less well defined, probably younger, SW direction with D = 237°, I = 6° (α₉₅= 9°, N = 8). Correction for dip of these two directions gives D = 329°, I =−7° (α₉₅= 10°) and D = 238°, I =−11° (α₉₅= 12°), respectively. The corresponding pole positions are P ₁ : 19° N, 225° E and P ₂: 19° S, 308° E, respectively. The reversed pole -P ₂ of the SW direction lies close to other NW European palaeomagnetic poles of Caledonian, Upper Silurian-Lower Devonian age. However, the dominant pole PI is far away from these, and could be due to a late Caledonian geomagnetic excursion of considerable duration; or it could record a c . 90° rotation around a vertical axis of a crustal block within the Scandinavian Caledonides. Block rotation could have been related to nappe translation, although geological observations do not at present appear to support the occurrence of such an event.     

Determination of earthquake early warning parameters, τc and Pd, for southern California

We explore a practical approach to earthquake early warning in southern California by determining a ground-motion period parameter  τ _c   and a high-pass filtered displacement amplitude parameter Pd from the initial 3 s of the P waveforms recorded at the Southern California Seismic Network stations for earthquakes with M > 4.0. At a given site, we estimate the magnitude of an event from  τ _c   and the peak ground-motion velocity ( PGV ) from Pd . The incoming three-component signals are recursively converted to ground acceleration, velocity and displacement. The displacements are recursively filtered with a one-way Butterworth high-pass filter with a cut-off frequency of 0.075 Hz, and a P -wave trigger is constantly monitored. When a trigger occurs,  τ _c   and Pd are computed. We found the relationship between  τ _c   and magnitude ( M ) for southern California, and between Pd and PGV for both southern California and Taiwan. These two relationships can be used to detect the occurrence of a major earthquake and provide onsite warning in the area around the station where onset of strong ground motion is expected within seconds after the arrival of the P wave. When the station density is high, the methods can be applied to multistation data to increase the robustness of onsite early warning and to add the regional warning approach. In an ideal situation, such warnings would be available within 10 s of the origin time of a large earthquake whose subsequent ground motion may last for tens of seconds.     

Absolute S-velocity estimation from receiver functions

We present a novel method to recover absolute S velocities from receiver functions.
For a homogeneous half-space the S velocity can be calculated from the horizontal slowness and the angle of surface particle motion for an incident P wave. Generally, the calculated S velocity is an apparent half-space value which depends on model inhomogeneity and P -waveform. We therefore, suggest to calculate such apparent half-space S velocities from low-pass filtered (smoothed) receiver functions using a suite of filter-parameters, T . The use of receiver functions neutralize the influence of the P -waveform, and the successive low-pass filterings emphasize the variation of S velocity with depth.
We apply this   V _{S ,app.}( T )  technique to teleseismic data from three stations: FUR, BFO and SUM, situated on thick sediments, bedrock and the Greenland ice cap, respectively. The observed   V _{S ,app.}( T )  curves indicate the absolute S velocities from the near surface to the uppermost mantle beneath each station, clearly revealing the different geological environments. Application of linearized, iterative inversion quantify these observations into   V _S ( z )  models, practically independent of the S -velocity starting model. The obtained models show high consistency with independent geoscientific results. These cases provide also a general validation of the   V _{S ,app.}( T )  method.
We propose the computation of   V _{S ,app.}( T )  curves for individual three-component broad-band stations, both for direct indication of the S velocities and for inverse modelling.     

Observation of Coriolis coupled modes below 1 mHz

We present observations of spectral energy at toroidal mode frequencies in vertical seismic recordings of the 1998 Balleny Islands earthquake. Since toroidal modes on a spherically symmetric, nonrotating Earth have horizontally polarized particle motion these observations call for an explanation. We first rule out local and instrumental effects as being responsible for the verticalcomponent signal of the toroidal modes ₀ T ₃ (0.59 mHz) and ₀ T ₄ (0.77 mHz). The global effects that we consider are general heterogeneous mantle structure, ellipticity of figure and rotation. We find that rotation through Coriolis coupling of loworder spheroidal and toroidal oscillations is the dominant mechanism.     

Core–mantle boundary deformations and J2 variations resulting from the 2004 Sumatra earthquake

The deformation at the core–mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core–mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field ( J ₂) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 10¹⁸ Pa s, the postseismic J ₂ variation in the next years is expected to leave a detectable signal in geodetic observations.     

Further evidence for oceanic excitation of polar motion

While the role of the atmosphere in driving variations in polar motion is well established, the importance of the oceans has been recognized only recently. Further evidence for the role of the oceans in the excitation of polar motion is presented. To estimate the equatorial excitation functions, χ ₁ and χ ₂ , for the ocean, we use velocity and mass fields from a constant-density ocean model, driven by observed surface wind stresses and atmospheric pressure, for the period 1993–1995; comparison with similar functions derived from a more complex density-stratified ocean model indicates the effectiveness of the simple constant-density modelling approach. Corresponding atmospheric excitation functions are computed from NCEP/NCAR re-analyses. Results indicate significant improvements in the agreement with the observed polar motion excitation when the simulated oceanic effects are added to atmospheric excitation. Correlations between the polar motion and the geophysical signals at periods of 15–150 days increase from 0.53 to 0.80 and from 0.75 to 0.88 for χ ₁ and χ ₂ , respectively. The oceanic signals are particularly important for seasonal variations in χ ₁ (correlation increases from 0.28 to 0.85 when oceanic excitation is included). A positive impact of the oceans on more rapid polar motion is also observed, up to periods as short as 5 days. The sensitivity of the results to different forcing fields and different amounts of friction in the oceans is also discussed.